CN103198500A - Compressed sensing image reconstruction method based on principal component analysis (PCA) redundant dictionary and direction information - Google Patents

Abstract

The invention discloses a compressed sensing image reconstruction method based on a principal component analysis (PCA) redundant dictionary and direction information. The compressed sensing image reconstruction method based on the PCA redundant dictionary and the direction information mainly solves the problem that in an existing compressed sensing reconstruction method OMP, a reconstructed image under a blocking compressed sensing framework has blocking effect and fuzzy texture. The compressed sensing image reconstruction method based on the PCA redundant dictionary and the direction information comprises the following steps: constructing the PCA redundant dictionary; receiving measurement matrixes and blocking measurement vector quantities, and judging category of an image block to be reconstructed according to each blocking measurement vector quantity; designing a species group initialization scheme and a sequencing cross operator based on the direction information on each image block to be reconstructed, and using a genetic algorithm and a clone selection algorithm to achieve reconstruction of each image block under the PCA redundant dictionary. Compared with an OMP method, the compressed sensing image reconstruction method based on the PCA redundant dictionary and the direction information has the advantages of being capable of seeking an optimum sparse representation of each image block from the overall situation under the PCA redundant dictionary, clear in texture and edge of the reconstructed image, and capable of being used for acquiring a high quality image in the process of reconstructing images under the blocking compressed sensing framework.

Description

Compressed sensing image reconstructing method based on PCA redundant dictionary and directional information

Technical field

The invention belongs to technical field of image processing, further relate to the compressed sensing image reconstructing method, be used in when original image recovered, obtain the image of high-resolution quality.

Background technology

In recent years, a kind of new data acquisition theory " compressed sensing " CS has appearred in the signal process field, this theory realizes compression in data acquisition, broken through the restriction of traditional nyquist sampling theorem, bring revolutionary variation for data acquisition technology, made this theory in fields such as compression imaging system, military cryptology, wireless sensings wide application prospect be arranged.The compressed sensing theory mainly comprises the rarefaction representation of signal, the observation of signal and three aspects such as reconstruct of signal.Aspect the signal rarefaction representation, dictionary commonly used has cosine dictionary, ridge ripple dictionary etc., aspect signal reconstruction, by finding the solution l ₀Or l ₁The optimization problem of norm is come reconstructed image.

People such as Tropp are " JoelA.Tropp; AnnaC.Gilbert, SignalRecoveryFromRandom MeasurementsViaOrthogonalMatchingPursuit " middle signal recovery method that proposes based on the random observation of orthogonal matching pursuit in the literature.This method is hanged down the random observation of sampling to sparse signal, from the former word bank of quadrature, select can the matched signal structure atom, thereby reconstruct image.The deficiency that this method exists is, in restructuring procedure, use greedy thought to seek the former sub-portfolio of rarefaction representation base, it is not the combination of seeking basic atom from the overall situation, thereby cause the image that reconstructs not accurate enough, and it has forced limited isometry RIP constraint to the compressed sensing framework, say in a sense, limited the range of application of compressed sensing.

The patented claim of Xian Electronics Science and Technology University " based on the block image compressed sensing reconstructing method of structure dictionary " (publication number: CN102708576A, application number: 201210155980.3, the applying date: disclose a kind of finding the solution by the image block sample on May 18th, 2012) and obtained redundant dictionary and be reconstructed.This method is at first classified to image block based on the architectural feature of image block, then with every class image block as training sample, utilize k-Singular ValueDecomposition (KSVD) dictionary training method to obtain the structure dictionary of redundant dictionary and cosine dictionary composition, when the piecemeal compressed sensing is rebuild, utilize the method based on the reconstruction error weighting to obtain final image at last.The deficiency that this patented claim exists is, although the rarefaction representation dictionary that uses is more redundant, but the combination at the basic atom of finding the solution rarefaction representation, use greedy thought, it is not very desirable finally causing image reconstruct effect, and training sample selects artificial the participation too much directly to influence the reconstruct of image.

In sum, based on l ₀In the compressed sensing reconstruct of norm, greedy algorithm can't obtain the former sub-portfolio of optimum rarefaction representation from the overall situation when finding the solution basic former sub-portfolio, and final reconstruct effect is not fine.Therefore, the research of compressed sensing reconstruct problem mainly concentrates on and how to construct better rarefaction representation dictionary and how to find the solution the rarefaction representation coefficient and accurately recover original signal under dictionary.

Summary of the invention

The objective of the invention is at observing under the less situation of number in the existing compressed sensing reconfiguration technique, greedy algorithm can not carry out effective rarefaction representation to picture signal, cause image texture information to be difficult to the shortcoming of accurate reconstruct, a kind of compressed sensing image reconstructing method based on PCA redundant dictionary and directional information is proposed, the quality of image after the raising reconstruct.

Realize that the object of the invention technical thought is: from the characteristic of PCA redundant dictionary, by design ordering crossover operator with based on the initialization of population scheme of directional information, genetic algorithm and Immune Clone Selection algorithm are organically combined as non-protruding compressed sensing optimization reconstructing method, be implemented in the combination of proceeding from the situation as a whole to find the solution the optimal base atom in the PCA redundant dictionary.Concrete steps comprise as follows:

(1) respectively excessively size be that 21 * 21 complete white image center is made straight line, generate 18 images of being cut apart by the Different Slope straight line, straight slope is taken from angle set { 10 * k+1|k=0 successively, 1,2 ... 17}, in every width of cloth split image, territory, the lateral areas value that will comprise summit, the image lower right corner is 1, opposite side zone value is 0, constructs the black white image of 18 directions;

(2) adopt the dot interlace method to select all pieces of 8 * 8 to the black white image of each direction respectively, obtain the training sample set { f of each direction _i} _k

(3) respectively to the training sample set { f of each direction _i} _kCarry out PCA and decompose, obtain the eigenvalue matrix S of each direction _kWith PCA orthogonal basis B _kAgain respectively to all PCA orthogonal basis B _kBe arranged in order by direction and obtain PCA redundant dictionary D and to all eigenvalue matrix S _kBe arranged in order by direction and obtain characteristic of correspondence value matrix E;

(4) input test image and be divided into 8 * 8 not overlapping block utilizes random Gaussian observing matrix A respectively each piece to be observed the measurement vector y that obtains each piece, and transmitting terminal sends the measurement vector y of observing matrix A and each piece, and receiving end receives;

(5) the measurement vector y of each piece of receiving is utilized the eigenvalue matrix S of 1 degree direction ₁With PCA orthogonal basis B ₁Carry out the image block classification and judge, smooth and non-smooth of mark;

(6) population scale being set is n=20, individual code length is K=16, and current evolutionary generation is p, and maximum evolutionary generation is mp, carry out different initialization of population operation with non-smooth according to directional information to smooth respectively, obtain parent population H (i)={ h of each image block i ₁(i) ..., h _l(i) ..., h _n(i) };

(7) respectively to the interlace operation of sorting of each individuality among the parent population H (i) of each piece, obtain progeny population H'(i);

(8) respectively to the progeny population H'(i of each piece) in each individuality carry out mutation operation;

(9) respectively to parent population H (i) and progeny population H'(i) in each individuality decode, obtain the former sub-portfolio D' of required PCA and corresponding sparse factor alpha, and calculate parent population H (i) and progeny population H'(i respectively) in each individual fitness; Fitness value is sorted the new population H''(i before selecting after the individuality composition heredity of n correspondence from big to small again);

(10) if current evolutionary generation p greater than the maximum evolutionary generation mp that arranges, execution in step (11) then, and keep new population H''(i after the heredity that finally obtains); Otherwise p=p+1 returns step (7);

(11) current clone's algebraically being set is q, and maximum clone's algebraically is mq, to the new population H''(i after the heredity) in each individuality carry out repeatedly replicate run, obtain the clone population G (i) of each individuality;

(12) each individuality among the clone population G (i) of each individuality is carried out mutation operation, obtain cloning the progeny population G'(i of population G (i));

(13) respectively to final population H''(i) in each individual corresponding clone population G (i) and progeny population G'(i) in each individuality decode, obtain the former sub-portfolio D' of required PCA and corresponding sparse factor alpha, and calculate final population H''(i) in each individual corresponding clone population G (i) and progeny population G'(i) in each individual fitness; The individuality that keeps the fitness maximum again, all the other individualities eliminate, the new population G''(i after obtaining cloning);

(14) if current clone's algebraically q greater than the termination clone algebraically mq that arranges, execution in step (15) then, and keep new population G''(i behind the clone who finally obtains of each image block i); Otherwise q=q+1 returns step (11);

(15) select the individuality of fitness maximum as the optimal base atom of each image block i the new population G''(i behind the clone who finally obtains of each image block i respectively), and obtain the image block of corresponding reconstruct with the sparse multiplication that the optimal base atom of each image block i is found the solution with it, again all images piece is arranged in order the image that obtains reconstruct.

Compared with prior art, the present invention has the following advantages:

First, the present invention proposes the direction base that in the compressed sensing field, uses PCA study any direction, the direction basis set that all direction study are obtained becomes just to have obtained PCA direction base redundant dictionary, when this dictionary direction is abundant, it can more sparse and adaptive expression any direction picture signal, overcome in the existing compressed sensing reconfiguration technique, orthogonal basis is the deficiency of rarefaction representation picture signal effectively, has improved the quality of reconstructed image.

Second, the present invention is from the characteristic of PCA redundant dictionary, by design ordering crossover operator with based on the initialization of population scheme of directional information, genetic algorithm and Immune Clone Selection algorithm organically combined as non-protruding compressed sensing optimize reconstructing method, obtained better image reconstruct effect.

The 3rd, the present invention reasonably combines directivity and the ordering interlace operation of PCA direction base, has solved the reconstruct problem of PCA direction base for the image block that has a plurality of directions, has promoted the image reconstruction quality.

Description of drawings

Fig. 1 is general flow chart of the present invention;

Fig. 2 is the sub-process figure that obtains dictionary among the present invention;

Fig. 3 is to be 40% o'clock emulation comparison diagram in sampling rate with the present invention and prior art;

Fig. 4 is the trend map that the Y-PSNR PSNR of the Barbara figure that comes out with the present invention and prior art reconstruct changes with sampling rate.

Embodiment

Below in conjunction with accompanying drawing the present invention is described further.

With reference to Fig. 1, concrete implementation step of the present invention is as follows:

Step 1 is obtained principal component analysis (PCA) PCA redundant dictionary

As shown in Figure 2, being implemented as follows of this step:

1.1) the structure black white image.

Cross size respectively and be 21 * 21 complete white image center and make straight line, generate 18 images of being cut apart by the Different Slope straight line, straight slope is taken from angle set { 10 * k+1|k=0 successively, 1,2 ... 17}, in every width of cloth split image, territory, the lateral areas value that will comprise summit, the image lower right corner is 1, opposite side zone value is 0, constructs the black white image of 18 directions;

1.2) the acquisition training sample.

Black white image to each direction adopts the dot interlace method to select all pieces of 8 * 8 respectively, obtains the training sample set { f of each direction _i} _k

1.3) acquisition PCA redundant dictionary.

1.3.1) respectively to the training sample set { f of each direction _i} _kCarry out PCA and decompose, obtain the eigenvalue matrix S of each direction _kWith PCA orthogonal basis B _k

1.3.1a) according to the training sample set { f of k direction _i} _k, obtain the covariance matrix ∑ of training sample set _kFor:

${\mathrm{\Σ}}_k=E\left[f_i{f}_i^T\right],$

Wherein, function E represents to find the solution the mathematical expectation of independent variable, f _iBe i the sample block that k direction training sample concentrated,

Be f _iTransposition;

1.3.1b) to the covariance matrix ∑ _kCarry out diagonalization, obtain PCA orthogonal basis and eigenvalue matrix, that is:

${\mathrm{\Σ}}_k=B_k{S}_k{B}_k^T,$

Wherein, B _kBe the PCA orthogonal basis of k direction,

Be B _kTransposition,

Be the eigenvalue matrix of k direction,

Be m eigenvalue of maximum on k the direction, m ∈ 1 ..., N}, N are the covariance matrix ∑s _kThe eigenwert number;

1.3.2) respectively to all PCA orthogonal basis B _kBe arranged in order by direction and obtain PCA redundant dictionary D and to all eigenvalue matrix S _kBe arranged in order by direction and obtain characteristic of correspondence value matrix E.

Step 2 receives observing matrix and measures vector.

The input test image also is divided into 8 * 8 not overlapping block, each not overlapping block of 8 * 8 is pulled into a column vector, obtain the column vector of each piece, utilize random Gaussian observing matrix A respectively the column vector of each piece to be observed, obtain the measurement vector y of each piece, transmitting terminal sends the measurement vector y of observing matrix A and each piece, and receiving end receives the measurement vector y of observing matrix A and each piece.

Step 3, the image block classification is judged.

3.1) the measurement vector y of each piece of receiving utilized the eigenvalue matrix S of 1 degree direction ₁With PCA orthogonal basis B ₁Calculate the sparse factor beta of the measurement vector y of each piece according to following formula,

β=((AB ₁) ^T(AB ₁)+σ ²(S ₁) ^-1) ^-1(AB ₁) ^Ty,

Wherein, A is observing matrix, and σ is control eigenvalue matrix S ₁To the parameter of the influence degree of sparse factor beta, and σ=3, the transposition of () T representing matrix, () ^-1Representing matrix contrary;

3.2) calculate the reconstructed error error of the measurement vector y correspondence of each piece according to following formula,

$\mathrm{error}={\left|\right|y-{\mathrm{AB}}_1\mathrm{\β}\left|\right|}_2^2$

Wherein,

Represent vectorial 2 norms square;

3.3) when reconstructed error error＜2.1, the image block that it is corresponding is labeled as smooth; Otherwise the image block that it is corresponding is labeled as non-smooth.

Step 4 is based on the initialization of population of directional information.

4.1) population scale is set is n=20, individual code length is K=16, and current evolutionary generation is p, and maximum evolutionary generation is mp, carries out different initialization of population operations to smooth with non-smooth respectively;

4.2) for smooth, then respectively the numbering in the basic atom place PCA redundant dictionary of first three eigenvalue of maximum correspondence of PCA orthogonal basis of each direction is added in the individual encoding gene position, all the other 13 gene position at random from the counterparty to PCA base atom place PCA redundant dictionary numbering in choose, to produce 18 individualities, two other individuality selects basic atom numbering as gene position at random from the PCA redundant dictionary;

4.3) for non-smooth, respectively the numbering in the basic atom place PCA redundant dictionary of the first eight eigenvalue of maximum correspondence of PCA orthogonal basis of each direction is added in the individual encoding gene position, all the other 8 gene position at random from the counterparty to PCA base atom place PCA redundant dictionary numbering in choose, to produce 18 individualities, two other individuality selects basic atom numbering as gene position at random from the PCA redundant dictionary; Obtain parent population H (i)={ h of each image block i ₁(i) ..., h _l(i) ..., h _n(i) }, h wherein _l(i) l individuality of i image block of expression, l ∈ 1 ..., n}.

Step 5 to the interlace operation of sorting of each individuality among the parent population H (i) of each piece, obtains progeny population H'(i respectively).

5.1) to the current individuality of parent population H (i) , produce equally distributed random number in [0,1] at first at random, if this random number smaller or equal to crossover probability Pc, is then selected body one by one at random from parent population H (i)

Individual as intersecting, execution in step (7b); Otherwise the interlace operation of not sorting, i ≠ j wherein, Pc=0.8, Represent current genes of individuals position, i _p∈ 1 ..., K},

Expression intersection genes of individuals position, j _p∈ 1 ..., K}, K are individual code lengths, and K=16;

5.2) with current individual h _iRearrange gene position according to characteristic of correspondence value order from small to large, the current individuality that obtains rearranging

To intersect individual h again _jRearrange gene position according to characteristic of correspondence value order from big to small, the intersection individuality that obtains rearranging

M wherein _p∈ { i ₁..., i _p... i _K, n _p∈ { j ₁..., j _p... j _K;

5.3) in [1, K] is interval, produce equally distributed random integers as the position, point of crossing, the current individuality to rearranging again

With the intersection individuality that rearranges

Use single-point to intersect the current individuality that is about to rearrange in the position, point of crossing

Gene place value after the position, point of crossing

With the intersection individuality that rearranges

Gene place value after the position, point of crossing

Exchange obtains new current individuality mutually With new intersection individuality After each individuality among the parent population H (i) finished the ordering interlace operation, the individual progeny population H'(i that forms of the current individuality that all that obtain are new and new intersection).

Step 6, variation.

6.1) respectively to filial generation population H'(i) and in each individual produces equally distributed random number in [0,1];

6.2) if certain individual random number corresponding smaller or equal to variation probability P m, is then carried out mutation operation to this individuality, namely produce equally distributed random integers in [1, K] at first at random, the gene position of indicating to make a variation with these random integers; From the PCA redundant dictionary, select a not basic atom numbering in this genes of individuals position more at random, substitute the gene place value that will make a variation, wherein Pm=0.2.

Step 7 is selected.

7.1) respectively to parent population H (i) and progeny population H'(i) and in each individuality decode, obtain the sub-dictionary D' of required PCA redundant dictionary and corresponding sparse factor alpha;

7.1a) find out the basic atom of all gene position correspondences of each individuality respectively, form sub-dictionary D' and eigenwert combination Σ ' that rarefaction representation uses:

$D^{\&prime;}=[d_{{\mathrm{<figure-callout\; id="1"\; label="i"\; filenames="HDA00003010619800021.png"\; state="\{\{state\}\}">i</figure-callout>}}_1},...,d_{i_p},...d_{i_K}],$

${\mathrm{\&Sigma;}}^{\&prime;}=\mathrm{diag}({\mathrm{\&lambda;}}_{i_1},...,{\mathrm{\&lambda;}}_{i_p},...{\mathrm{\&lambda;}}_{i_K}),$

Wherein,

Be the i of certain individuality _pThe basic atom of individual gene position correspondence,

Be

The characteristic of correspondence value, diag represent with Form a diagonal matrix, i as the element on the diagonal line _p∈ 1 ..., K};

7.1b) obtain the sparse factor alpha of each individuality according to following formula:

$\mathrm{\&alpha;}={({\left({\mathrm{AD}}^{\&prime;}\right)}^T\left({\mathrm{AD}}^{\&prime;}\right)+{\widetilde{\mathrm{\&sigma;}}}^2{\left({\mathrm{\&Sigma;}}^{\&prime;}\right)}^{-1})}^{-1}{\left({\mathrm{AD}}^{\&prime;}\right)}^{T}y,$

Wherein, Be that the control eigenwert makes up Σ ' to the parameter of the influence degree of sparse factor alpha, and

() ^TThe transposition of representing matrix, () ^-1Representing matrix contrary;

7.2) utilize sparse factor alpha and the sub-dictionary D' of each individuality that decoding obtains to calculate each individual fitness f (D') according to following formula respectively:

$f\left(D^{\&prime;}\right)=1/{\left|\right|y-{\mathrm{AD}}^{\&prime;}\mathrm{\&alpha;}\left|\right|}_2^2,$

Wherein, Represent vectorial 2 norms square;

7.3) all fitness values are sorted from big to small the new population H''(i before selecting after the individuality composition heredity of n correspondence).

Step 8 is judged whether termination of iterations of genetic algorithm.

If current evolutionary generation p is greater than the maximum evolutionary generation mp that arranges, then execution in step nine, and keep the new population H''(i after the heredity that finally obtains); Otherwise p=p+1 returns step 5.

Step 9, the clone.

It is q that current clone's algebraically is set, and maximum clone's algebraically is mq, to the new population H''(i after the heredity) in each individuality carry out repeatedly replicate run, obtain the clone population G (i) of each individuality.

Step 10 is carried out mutation operation to each individuality among the clone population G (i) of each individuality, obtains cloning the progeny population G'(i of population G (i)).

10.1) each individuality among the clone population G (i) of each individuality is produced equally distributed random integers in [1, K] at random, the gene position of indicating to make a variation with these random integers;

10.2) obtain the direction k at the gene position place that will make a variation, from the PCA orthogonal basis B corresponding with direction k _kIn select a not numbering of the basic atom in this genes of individuals position at random, substitute the gene place value that will make a variation; After each individuality among clone population G (i) finished mutation operation, obtain cloning the progeny population G'(i of population G (i)).

Step 11, Immune Clone Selection.

11.1) respectively to the new population H''(i after the heredity) and in each individual corresponding clone population G (i) and progeny population G'(i) in each individuality decode, obtain the sub-dictionary D' of required PCA redundant dictionary and the sparse factor alpha of correspondence;

11.1a) find out the basic atom of all gene position correspondences of each individuality respectively, form sub-dictionary D'' and eigenwert combination Σ ' ' that rarefaction representation uses:

$D^{\&prime;\&prime;}=[d_{i_1}^{\&prime;},...,d_{i_p}^{\&prime;},...d_{i_K}^{\&prime;}],$

${\mathrm{\&Sigma;}}^{\&prime;\&prime;}=\mathrm{diag}({\mathrm{\&lambda;}}_{i_1}^{\&prime;},...,{\mathrm{\&lambda;}}_{i_p}^{\&prime;},...{\mathrm{\&lambda;}}_{i_K}^{\&prime;}),$

Wherein, Be the i of certain individuality _pThe basic atom of individual gene position correspondence,

Be

The characteristic of correspondence value, diag represent with

Form a diagonal matrix, i as the element on the diagonal line _p∈ 1 ..., K};

11.1b) obtain the sparse factor alpha of each individuality according to following formula:

$\mathrm{\&alpha;}={({\left({\mathrm{AD}}^{\&prime;\&prime;}\right)}^T\left({\mathrm{AD}}^{\&prime;\&prime;}\right)+{\widehat{\mathrm{\&sigma;}}}^2{\left({\mathrm{\&Sigma;}}^{\&prime;\&prime;}\right)}^{-1})}^{-1}{\left({\mathrm{AD}}^{\&prime;\&prime;}\right)}^{T}y$

Wherein,

Be that the control eigenwert makes up Σ ' ' to the parameter of the influence degree of sparse factor alpha, and

() ^TThe transposition of representing matrix, () ^-1Representing matrix contrary;

11.2) utilize sparse factor alpha and the sub-dictionary D'' of each individuality that decoding obtains to calculate each individual fitness f (D'') according to following formula respectively:

$f\left(D^{\&prime;\&prime;}\right)=1/{\left|\right|y-{\mathrm{AD}}^{\&prime;\&prime;}\mathrm{\&alpha;}\left|\right|}_2^2,$

Wherein,

Represent vectorial 2 norms square;

11.3) keep the individuality of fitness maximum, all the other individualities eliminate, the new population G''(i after obtaining cloning).

Step 12 is judged whether termination of iterations of clone algorithm.

If current clone's algebraically q is greater than the termination clone algebraically mq that arranges, then execution in step 13, and keep the new population G''(i behind the clone who finally obtains of each image block i); Otherwise q=q+1 returns step 9.

Step 13 obtains reconstructed image.

New population G''(i behind the clone who finally obtains of each image block i respectively) select the individuality of fitness maximum as the optimal base atom of each image block i in, and obtain the image block of corresponding reconstruct with the sparse multiplication that the optimal base atom of each image block i is found the solution with it, again all images piece is arranged in order the image that obtains reconstruct.

Effect of the present invention can further specify by following emulation.

1. simulated conditions:

Emulation of the present invention is at windowsXP, and SPI, CPUPentium (R) 4, basic frequency 2.4GHZ, software platform are that MatlabR2007 goes up operation, and emulation is selected for use is 512 * 512 standard Barbara and Lena image.

2. emulation content and result:

(1) emulation 1:

In this emulation, use orthogonal matching pursuit OMP and the inventive method are 512 * 512 standard Barbara and Lena image to size, be in sampling rate under 40% the condition and carry out image reconstruct, the dictionary that the OMP algorithm uses is dictionary of the present invention, rarefaction representation coefficient method for solving is the same with the present invention, and reconstruction result as described in Figure 3.Wherein:

Fig. 3 (a) is the Barbara original image,

Fig. 3 (b) is Lena original image figure,

Fig. 3 (c) is the Barbara that obtains of algorithm of the present invention figure as a result,

Fig. 3 (d) is the Lena that obtains of algorithm of the present invention figure as a result,

Fig. 3 (e) is the Barbara partial enlarged drawing that algorithm of the present invention obtains,

Fig. 3 (f) is the Lena partial enlarged drawing that algorithm of the present invention obtains,

Fig. 3 (g) is the Barbara that obtains of OMP algorithm figure as a result,

Fig. 3 (h) is the Lena that obtains of OMP algorithm figure as a result,

Fig. 3 (i) is the Barbara partial enlarged drawing that the OMP algorithm obtains,

Fig. 3 (j) is the Lena partial enlarged drawing that the OMP algorithm obtains.

From reconstruction result figure especially partial enlarged drawing as can be seen, the present invention has greatly improved at the image reconstruction quality, especially in Barbara trousers texture and Lena hair reconstruction result clearly as can be seen.

(2) emulation 2:

In this emulation, be the Barbara image to be carried out emulation at 25%, 30%, 35%, 40%, 45% o'clock in sampling rate respectively with existing OMP and the inventive method, obtain accurate Y-PSNR PSNR, as shown in table 1.

PSNR value under each sampling rate of table 1

From table 1 data as can be seen, method of the present invention is that the Y-PSNR PSNR of the figure as a result that obtains for 25%, 30%, 35%, 40%, 45% time will be higher than the PSNR that the OMP method obtains in sampling rate, and namely the reconstructed image quality of method of the present invention is than OMP method height.

Obtain the trend map that the PSNR of the Barbara figure that OMP method and the inventive method reconstruct changes with sampling rate according to table 1 data, its result as shown in Figure 4, the horizontal ordinate among Fig. 4 is represented sampling rate, ordinate is represented Y-PSNR PSNR (dB) value.

As seen from Figure 4, the PSNR value of the reconstruction result figure that obtains of the inventive method is apparently higher than additive method.

To sum up, the present invention is texture and the marginal portion of reconstructed image well, obtains distinct image, compares with existing other reconstructing methods, and the present invention has improved the reconstruction quality of image.

Claims (8)

1. the compressed sensing image reconstructing method based on PCA redundant dictionary and directional information comprises the steps:

(1) respectively excessively size be that 21 * 21 complete white image center is made straight line, generate 18 images of being cut apart by the Different Slope straight line, straight slope is taken from angle set { 10 * k+1|k=0 successively, 1,2 ... 17}, in every width of cloth split image, territory, the lateral areas value that will comprise summit, the image lower right corner is 1, opposite side zone value is 0, constructs the black white image of 18 directions;

(2) adopt the dot interlace method to select all pieces of 8 * 8 to the black white image of each direction respectively, obtain the training sample set { f of each direction _i} _k

(3) respectively to the training sample set { f of each direction _i} _kCarry out PCA and decompose, obtain the eigenvalue matrix S of each direction _kWith PCA orthogonal basis B _kAgain respectively to all PCA orthogonal basis B _kBe arranged in order by direction and obtain PCA redundant dictionary D and to all eigenvalue matrix S _kBe arranged in order by direction and obtain characteristic of correspondence value matrix E;

(4) input test image and be divided into 8 * 8 not overlapping block utilizes random Gaussian observing matrix A respectively each piece to be observed the measurement vector y that obtains each piece, and transmitting terminal sends the measurement vector y of observing matrix A and each piece, and receiving end receives;

(5) the measurement vector y of each piece of receiving is utilized the eigenvalue matrix S of 1 degree direction ₁With PCA orthogonal basis B ₁Carry out the image block classification and judge, smooth and non-smooth of mark;

(6) population scale being set is n=20, individual code length is K=16, and current evolutionary generation is p, and maximum evolutionary generation is mp, carry out different initialization of population operation with non-smooth according to directional information to smooth respectively, obtain parent population H (i)={ h of each image block i ₁(i) ..., h _l(i) ..., h _n(i) };

(7) respectively to the interlace operation of sorting of each individuality among the parent population H (i) of each piece, obtain progeny population H'(i);

(8) respectively to the progeny population H'(i of each piece) in each individuality carry out mutation operation;

(9) respectively to parent population H (i) and progeny population H'(i) in each individuality decode, obtain the former sub-portfolio D' of required PCA and corresponding sparse factor alpha, and calculate parent population H (i) and progeny population H'(i respectively) in each individual fitness; Fitness value is sorted the new population H''(i before selecting after the individuality composition heredity of n correspondence from big to small again);

(10) if current evolutionary generation p greater than the maximum evolutionary generation mp that arranges, execution in step (11) then, and keep new population H''(i after the heredity that finally obtains); Otherwise p=p+1 returns step (7);

(11) current clone's algebraically being set is q, and maximum clone's algebraically is mq, to the new population H''(i after the heredity) in each individuality carry out repeatedly replicate run, obtain the clone population G (i) of each individuality;

(12) each individuality among the clone population G (i) of each individuality is carried out mutation operation, obtain cloning the progeny population G'(i of population G (i));

(13) respectively to final population H''(i) in each individual corresponding clone population G (i) and progeny population G'(i) in each individuality decode, obtain the former sub-portfolio D' of required PCA and corresponding sparse factor alpha, and calculate final population H''(i) in each individual corresponding clone population G (i) and progeny population G'(i) in each individual fitness; The individuality that keeps the fitness maximum again, all the other individualities eliminate, the new population G''(i after obtaining cloning);

(14) if current clone's algebraically q greater than the termination clone algebraically mq that arranges, execution in step (15) then, and keep new population G''(i behind the clone who finally obtains of each image block i); Otherwise q=q+1 returns step (11);

(15) select the individuality of fitness maximum as the optimal base atom of each image block i the new population G''(i behind the clone who finally obtains of each image block i respectively), and obtain the image block of corresponding reconstruct with the sparse multiplication that the optimal base atom of each image block i is found the solution with it, again all images piece is arranged in order the image that obtains reconstruct.

2. the compressed sensing image reconstructing method based on PCA redundant dictionary and directional information according to claim 1, wherein, the training sample { f to each direction in the described step (3) _i} _kCarry out PCA and decompose, carry out as follows:

(3a) according to the training sample set { f of k direction _i} _k, obtain the covariance matrix ∑ of training sample set _kFor:

$E_k=E\left[f_i{f}_i^T\right],$

Wherein, function E represents to find the solution the mathematical expectation of independent variable, f _iBe i the sample block that k direction training sample concentrated,

Be f _iTransposition;

(3b) to the covariance matrix ∑ _kCarry out diagonalization, obtain PCA orthogonal basis and eigenvalue matrix, that is:

${\mathrm{\&Sigma;}}_k=B_k{S}_k{B}_k^T,$

Wherein, B _kBe the PCA orthogonal basis of k direction,

Be B _kTransposition, Be the eigenvalue matrix of k direction,

Be m eigenvalue of maximum on k the direction, m ∈ 1 ..., N}, N are the covariance matrix ∑s _kThe eigenwert number.

3. the compressed sensing image reconstructing method based on PCA redundant dictionary and directional information according to claim 1, wherein, carry out different initialization of population operation with non-smooth according to directional information to smooth respectively in the described step (6), carry out as follows:

(6a) population scale being set is n=20, and individual code length is K=16, carries out different initialization of population operations to smooth with non-smooth respectively;

(6b) for smooth, then respectively the numbering in the basic atom place PCA redundant dictionary of first three eigenvalue of maximum correspondence of PCA orthogonal basis of each direction is added in the individual encoding gene position, all the other 13 gene position at random from the counterparty to PCA base atom place PCA redundant dictionary numbering in choose, to produce 18 individualities, two other individuality selects basic atom numbering as gene position at random from the PCA redundant dictionary;

(6c) for non-smooth, respectively the numbering in the basic atom place PCA redundant dictionary of the first eight eigenvalue of maximum correspondence of PCA orthogonal basis of each direction is added in the individual encoding gene position, all the other 8 gene position at random from the counterparty to PCA base atom place PCA redundant dictionary numbering in choose, to produce 18 individualities, two other individuality selects basic atom numbering as gene position at random from the PCA redundant dictionary.

4. the compressed sensing image reconstructing method based on PCA redundant dictionary and directional information according to claim 1, wherein, the ordering interlace operation in the described step (7), carry out as follows:

(7a) to the current individuality of parent population H (i)

Produce equally distributed random number in [0,1] at first at random, if this random number smaller or equal to crossover probability Pc, is then selected body one by one at random from parent population H (i)

Individual as intersecting, execution in step (7b); Otherwise the interlace operation of not sorting, i ≠ j wherein, Pc=0.8, Represent current genes of individuals position, i _p∈ 1 ..., K},

Expression intersection genes of individuals position, j _p∈ 1 ..., K}, K are individual code lengths, and K=16;

(7b) with current individual h _iRearrange gene position according to characteristic of correspondence value order from small to large, the current individuality that obtains rearranging

To intersect individual h again _jRearrange gene position according to characteristic of correspondence value order from big to small, the intersection individuality that obtains rearranging

M wherein _p∈ { i ₁..., i _p... i _K, n _p∈ { j ₁..., j _p... j _K;

(7c) in [1, K] is interval, produce equally distributed random integers as the position, point of crossing, the more current individual h ＇ to rearranging _iWith the individual h ＇ of the intersection that rearranges _jUse single-point to intersect in the position, point of crossing, obtain new current individuality

With new intersection individuality

5. the compressed sensing image reconstructing method based on PCA redundant dictionary and directional information according to claim 1, wherein, the mutation operation in the described step (8), carry out as follows:

(8a) respectively to filial generation population H'(i) in each individual produces equally distributed random number in [0,1];

If (8b) certain individual random number corresponding is then carried out mutation operation to this individuality smaller or equal to variation probability P m, namely produce equally distributed random integers in [1, K] at first at random, the gene position of indicating to make a variation with these random integers; From the PCA redundant dictionary, select a not basic atom numbering in this genes of individuals position more at random, substitute the gene place value that will make a variation, wherein Pm=0.2.

6. the compressed sensing image reconstructing method based on PCA redundant dictionary and directional information according to claim 1, wherein, the decode operation in the described step (9), carry out as follows:

(9a) find out the basic atom of all gene position correspondences of each individuality respectively, form sub-dictionary D' and eigenwert combination Σ ' that rarefaction representation uses:

$D^{\&prime;}=[d_{i_1},...,d_{i_p},...d_{i_K}],$

${\mathrm{\&Sigma;}}^{\&prime;}=\mathrm{diag}({\mathrm{\&lambda;}}_{i_1},...,{\mathrm{\&lambda;}}_{i_p},...{\mathrm{\&lambda;}}_{i_K}),$

Wherein,

Be the i of certain individuality _pThe basic atom of individual gene position correspondence,

Be

The characteristic of correspondence value, diag represent with

Form a diagonal matrix, i as the element on the diagonal line _p∈ 1 ..., K}.

(9b) obtain the sparse factor alpha of each individuality according to following formula:

α=((AD') ^T(AD')+σ ²(Σ') ^-1) ^-1(AD') ^Ty

Wherein, A is observing matrix, and y is the measurement vector of the image block of each individual correspondence, and σ is that the control eigenwert makes up Σ ' to the parameter of the influence degree of sparse factor alpha, and σ=3, σ ²Be σ square, () ^TThe transposition of representing matrix, () ^-1Representing matrix contrary.

7. the compressed sensing image reconstructing method based on PCA redundant dictionary and directional information according to claim 1, wherein, the calculating of the fitness in the described step (9) is to utilize sparse factor alpha and the sub-dictionary D' of each individuality that decoding obtains to calculate each individual fitness f (D') according to following formula:

$f\left(D^{\&prime;}\right)=1/{\left|\right|y-{\mathrm{AD}}^{\&prime;}\mathrm{\&alpha;}\left|\right|}_2^2$

Wherein, A is observing matrix, and y is the measurement vector of the image block of each individual correspondence,

Represent vectorial 2 norms square.

8. the compressed sensing image reconstructing method based on PCA redundant dictionary and directional information according to claim 1, wherein, the mutation operation in the described step (12), carry out as follows:

(12a) each individuality among the clone population G (i) of each individuality is produced equally distributed random integers in [1, K] at random, the gene position of indicating to make a variation with these random integers;

(12b) obtain the direction k at the gene position place that will make a variation, from the PCA orthogonal basis B corresponding with direction k _kIn select a not numbering of the basic atom in this genes of individuals position at random, substitute the gene place value that will make a variation.

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